# FISICA I F - O

**Academic Year 2024/2025**- Teacher:

**MARIA JOSE' IRENE LO FARO**

## Expected Learning Outcomes

**knowledge and understanding:**knowledge of the foundations of classical mechanics and thermodynamics, including their mathematical description;**ability to apply knowledge and understanding:**develop and/or improve the ability to recognize the main physical laws that describe a mechanical or thermodynamic phenomenon; and to apply such laws to solve physics problems through the use of appropriate analytical and numerical techniques;**making judgments:**provide the tools to estimate the order of magnitude of the variables describing a mechanical or thermodynamic phenomenon and estimate the "level of importance" (e.g. conservation principle, universal law, theorem, etc. .) of a physical law;**communication skills:**develop and/or improve the ability to present scientific concepts with technical language properties;**learning skills:**knowing how to apply theoretical-mathematical techniques and models to Physics and knowing how to find the correct sources.

## Course Structure

The teaching method is generally the most congenial to the teaching of Physics 1. In particular, in addition to the classical lecture with the use of a standard blackboard, slides will be used to deepen some specific topics. In addition, multimedia files (video and / or audio) will be used to facilitate the understanding of some topics. In addition to this, teaching in cooperative learning is privileged, in which the classroom becomes a moment of development and apprehension of knowledge. Brainstorming will also be considered (mainly for the resolution of exercises submitted by the teacher) and flipped-classroom in which the students will be directly called into question to explain or illustrate exercises or theoretical topics. The verification method includes self-assessment tests during the entire semester, as well as exam tests with exercises on the course topics.

*Should the circumstances require online
or blended teaching, appropriate modifications to what is hereby stated may be
introduced, in order to achieve the main objectives of the course.
Additionally, exams may take place online, depending on circumstances.*

*Information
for students with disabilities and / or SLD: *To
guarantee equal opportunities and in compliance with the laws in force,
interested students can ask for a personal interview in order to plan any
compensatory and/or dispensatory measures, based on the didactic objectives and
specific needs. It is also possible to contact the referent teacher CInAP
(Center for Active and Participatory Integration - Services for Disabilities
and / or SLD) of our Department, prof. A. Pagano.

## Required Prerequisites

- ability in algebraic calculation;
- familiarity with differential calculus;
- knowledge of trigonometry;
- knowledge of the main geometric laws;
- familiarity with the study of mathematical functions.

## Attendance of Lessons

As a rule, the student is required to attend at least 70% of the hours of each course, without prejudice to the provisions of the art. 27 of the R.D.A. and by the Regulation for the recognition of the status of student worker, student athlete, student in difficulty and student with disabilities (D.R. n. 1598 of 2/5/2018).

## Detailed Course Content

**Physical quantities and units of measurement.** The scientific method. Physical quantities and units of measure. The International System (SI). Scientific notation. Dimensional issues. Fundamental quantities and derived quantities. Measurement errors and approximations. Significant figures. Function approximations.

**Scalars and vectors. **Scalar and vector quantities. Invariance and symmetry. Vector algebra. Vector analysis: derivatives and integrals of vectors.

**Kinematics.** Speed, acceleration, and hourly law of motion. Smooth and uniformly accelerated rectilinear motion. Vertical motion. Simple harmonic motion. Rectilinear motion damped exponentially. Plane motion: speed and acceleration. Circular motion. Parabolic motion. Motions in space.

**Physical quantities and measure units. **The scientific method. Physical quantities and measure units. The International System of Units (SIU). Scientific notation. Dimensionality. Fundamental quantities and derived quantities. Measurement of errors and approximations. Significant figures. Approximation of mathematical functions.

**Vector calculus. **Scalar quantities and vectors. Invariance and symmetry of systems. Vector calculus: algebra, derivatives and integrals with vectors.

**Kinematics.** Equations of motion. Linear motion and uniformly accelerated linear motion. Vertical motion. Harmonic oscillator. Damped linear motion. Motion in a plane: velocity and acceleration. Circular and parabolic motion. Motion in the space.

**Dynamics of point particles.** Newton’s laws. Impulse (step) and momentum. Sum and equilibrium of forces. Examples: weight, friction, viscosity, centripetal force, elastic force, and Hook’s law. Inclined plane. Pendulum. Tension. Frames of reference. Relative velocity and acceleration. Inertial frames of reference. Galilean invariance.

**Work and energy. **Work, power, and kinetic energy. Theorem of kinetic energy and examples. Conservative forces and potential energy. Non-conservative forces. Conservation of energy. Force vs potential energy. Angular momentum. Central forces.

**Systems of point particles. **Systems of n point particles. Internal and external forces. Centre of mass. Conservation of momentum. Conservation of angular momentum. König’s theorem. Kinetic energy theorem.

**Rigid body dynamics. **Properties of a rigid body. Motion of a rigid body. Continuous distribution of mass, density and position of the body mass. Rigid rotations in three dimensions in an inertial frame of reference. Energy and virtual work of forces. Inertia. Huygens-Steiner’s theorem. Pendulum. Pure rolling. Conservation of energy in the motion of a rigid body. Rolling resistance.

**Oscillators and waves. **Differential equation of a harmonic oscillator. Equation of motion and solution for a simple harmonic oscillator. Mass-spring system: a simple harmonic oscillator. Energy of a simple harmonic oscillator. Sum of harmonic oscillators in one and two dimensions. Damped and driven harmonic oscillators. Resonance.

**Fluid mechanics. **Fluids. Pressure. Static equilibrium. Archimede’s principle. Internal friction and ideal fluid’s viscosity. Fluid flow: steady and unsteady flow. Flow rate. Bernoulli’s theorem. Torricelli’s theorem. Pascal’s principle. Laminar vs turbulent flow.

**Thermodinamics. **Temperature and the zeroth law of thermodynamics; Thermic contact; Thermometers; Absolute scale of temperatures; Thermic equilibrium; The heat; Thermal expansion of solids and liquids; Specific heat and calorimetry; Temperature of equiibrium; Latenet heat; The first law of thermodynamics; Work, heat and internal energy in thermodynamics; Transformation; Peferct gases; Transformations with constant temperature or volume or pressure; Molar specifi heat; The Mayer relation; Adiabatic transformations; The Carnot Cycle; The Carnot principle; The second law of thermodynamics; Entropy; Third law of thermodynamics

**Gravity. **Central forces. Kepler’s laws. Newton’s law of universal gravitation. Inertia vs gravitational mass. Gravitational fields and gravitational potential energy.

## Textbook Information

The material provided in class does not replace the textbook. A good Physics I textbook is essential for consolidating learning.

**P.Mazzoldi, M. Nigro, C. Voci: “**, II edizione, casa editrice EdiSES;__Elementi di Fisica”__Meccanica e Termodinamica**Halliday, Resnick, Krane,**, Casa editrice Ambrosiana__Fisica 1__- R. Serwey, J. Jewett:
, Vol.I, V Edizione,casa editrice EdiSES;*Fisica per Scienze ed Ingegneria* - Focardi S., Massa I., Uguzzoni A., Villa M. -
, Casa editrice Ambrosiana;*Fisica generale - MECCANICA E TERMODINAMICA*

## Course Planning

Subjects | Text References | |
---|---|---|

1 | PHYSICAL DESCRIPTION OF REALITY: physical quantities (general information on physics and physical quantities, units of measurement, errors, accuracy and precision of a measurement) | Testo 2: Appendice A,Testo 3: Appendice B |

2 | VECTOR CALCULATION: Vectors (general information on vector algebra, properties of the sum, Cartesian representation of vectors in 2D and 3D, scalar and vector product) | Testo 2: Appendice B,D, Capitolo 3. Testo 3: Appendice C |

3 | KINEMATICS OF THE SINGLE PARTICLE: Kinematics of material points (general information on the kinematics of the material point, average and instantaneous speed, average and instantaneous acceleration, uniform rectilinear motion, uniformly accelerated motion, parabolic motion, relative motion between 2 points, relativity and Galilean transformations) | Testo 2: Capitolo 4-6. Testo 3: Capitolo 1,2,5 |

4 | ''VARIOUS'' MOTIONS: Dynamics of material points - part II (exponentially damped rectilinear motion, viscous friction force, integral form of Newton's II law) + Rotational mechanics - part I (circular motion, centripetal and tangential acceleration, vector quantities rotational, moment of a force, inertial and non-inertial reference systems, apparent forces) | Testo 2: Capitolo 4-6.Testo 3: Capitolo 1-5 |

5 | DYNAMICS OF THE SINGLE PARTICLE: Dynamics of material points - part I (general information on the dynamics of the point, Newton's laws, momentum, static and dynamic equilibrium, constraint reactions, weight force, sliding friction force, inclined plane) + Oscillations - part I (simple harmonic motion: elastic force, one-dimensional harmonic oscillator, mass-spring system) | Testo 3: Capitolo 1,3 |

6 | WORK, POWER AND ENERGY: Mechanical energy and conservative systems (work, power, kinetic and potential energy for a material point; conservation of mechanical energy; work and potential energy for weight, elastic and constant forces; work of the sliding friction force) | Testo 2. Capitolo 7. Testo 3: Capitolo 4 |

7 | OSCILLATOR PHENOMENA: Oscillations - part II (simple pendulum, damped harmonic oscillator, forced harmonic oscillator) | Testo 2: Capitolo 15-18. Testo 3: Capitolo 3,10 |

8 | RIGID BODY DYNAMICS: Rigid body + Rotational mechanics - part II (moment of inertia, Huygens-Steiner theorem, combined translation and rotation motions, rolling friction, moment of impulse theorem for rigid bodies) + Oscillations - part III ( physical pendulums) + Elasticity (deformations of solid bodies, elastic constants, torsion pendulum) | Testo 2: Capitolo 10-12. Testo 3: Capitolo 7 |

9 | GRAVITATION: Central Forces Kepler's Laws. The Law of Universal Gravitation. Inertial mass and gravitational mass. Gravitational field and gravitational potential energy. | Testo 2: Capitolo 13, Testo 3: Capitolo 11 |

10 | DYNAMICS OF SYSTEMS OF MATERIAL POINTS: Collisions and systems of material points (general information on systems of material points, internal and external forces, center of mass, theorem of motion of the center of mass and of the angular momentum, reference system of the center of mass, Koenig's theorems for angular momentum and kinetic energy, kinetic energy theorem for a system of points, shock phenomena and impulsive forces, collisions between 2 bodies) | Testo 3: Capitolo 6,8 |

11 | FLUIDOSTATICS AND FLUID DYNAMICS: Fluids: liquids and gaseous. The perfect fluid modeling. Average and absolute density for a fluid, relative density. Pressure and unit of measure, shear stress. Fundamental equation of fluid statics; Stevino's law; Torricelli's experience; Pascal's Principle; trend of atmospheric pressure with altitude; the principle of Archimedes. Lagrangian and Eulerian description for moving fluids. Stationary regime. | Testo 2: Capitolo 14 |

12 | Thermodynamics | Mazzoldi, Nigro, Voci: “Fisica Vol. 1 – Meccanica e Termodinamica. Seconda edizione.” (EdiSES) & D. Halliday, R. Resnick, J. Walker ''Fondamenti di Fisica'' (2015) Casa Ed. Ambrosiana |

## Learning Assessment

### Learning Assessment Procedures

The course consists of 42 hours (6 CFU) of theoretical lessons held by the undersigned and 45 hours (3 CFU) of exercises with another teacher.

The exam consists of a written test + oral test. The final grade will take into account the tests passed by the candidates. NO EXEMPTION or ONGOING TESTS are foreseen due to too many overlaps with the other courses.

Exams will be performed online should the conditions require it.

**WRITTEN EXAM :**

For the written test, 2 exam sessions are scheduled in the 1st exam session period, 2 exam sessions in the 2nd exam session period and 2 exam sessions in the 3rd exam session period. There are also 2 exam sessions reserved for students who are out of course and latecomers (paragraphs 5 and 5 bis of the university teaching regulations) during the suspension of teaching activities, generally in the April/May or November/December period. No further appeals are foreseen beyond those approved by the teaching secretariat. Each student* can only participate in the sessions for which they are able to book.

The written test consists of solving 4 exercises:

- kinematics,
- point dynamics, system dynamics,
- fluid dynamics e
- thermodynamics.

The resolution of each problem will be assigned a score between 0/30 and 7.5/30 in relation to (1) the completeness of the description of the Physical and Mathematical Model used for the resolution, (2) the correctness of the mathematical treatment and, naturally , (3) the correctness of the result, both from a numerical and dimensional point of view.

Passing the written test with a minimum score of 18/30 allows access to the oral test. Students who obtain a score lower than 18/30 in the test are advised not to take the oral test. For scores greater than or equal to 15/30 and less than 18/30, the oral test is preceded by an interview to evaluate the candidate's basic knowledge.

**ORAL EXAM :**

If the written test is passed, the student will have to take the oral test NO LATER than the end of the exam session in which he took the written test, after which the written exam will be CANCELLED.

Typically the oral exam is carried out within a maximum of 14 days after the written exam, therefore it is recommended to acquire a good preparation of the subject already for the written exam.

In case of a negative result in the oral test, applicants MUST repeat the written exam.

The results of the written exam and the dates of the oral exam will be communicated for each session by means of a notice on the Smart EDU GOMP platform for those who have booked.

### Examples of frequently asked questions and / or exercises

For the written test, the old exam tasks will be provided, some will be done in class.

For the oral test some standard questions are reported:

- Discuss the inertial and non-inertial reference systems, presenting some real examples.
- Prove Bernoulli's theorem.
- Discuss the principles of conservation of mechanical energy, momentum, and angular momentum;
- Treat the principles of thermodynamics with the necessary applications;
- State and apply the second law of thermodynamics;
- Obtain the Bernoulli equation for an ideal fluid;
- Describe the motion of the simple pendulum, the mass-spring system, and a rigid body.
- Treatment of a thermodynamic cycle.

**VERSIONE IN ITALIANO**